Random, nonuniform distribution of line segments on a circle

DOI10.1016/0304-4149(84)90298-9zbMath0558.60016OpenAlexW2069652934MaRDI QIDQ762828

Hall, Peter

Publication date: 1984

Published in: Stochastic Processes and their Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0304-4149(84)90298-9

zbMATH Keywords

order statisticsasymptotic behaviourspacingscentral limit theoremline segments

Mathematics Subject Classification ID

Geometric probability and stochastic geometry (60D05) Central limit and other weak theorems (60F05) Stochastic processes (60G99) Packing and covering in (n) dimensions (aspects of discrete geometry) (52C17)

Related Items (6)

Three limit theorems for vacancy in multivariate coverage problems ⋮ Minimal spacings of non-uniform densities ⋮ Divisible statistics ⋮ On the longest gap between power-rate arrivals ⋮ Circles of equal radii randomly placed on a plane: some rigorous results, asymptotic behavior, and application to transparent electrodes ⋮ Limiting distribution of the maximal spacing when the density function admits a positive minimum

Cites Work

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• On convergence of the coverage by random arcs on a circle and the largest spacing
• Asymptotic coverage distributions on the circle
• Random circles on a sphere
• On the lengths of the pieces of a stick broken at random
• Random coverage of the circle and asymptotic distributions
• Random arcs on the circle
• Random space filling and moments of coverage in geometrical probability
• Moments of coverage and coverage spaces

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